Heat the olive oil in a medium wide pot over medium heat and cook the onion until wilted, about 8 minutes, stirring occasionally. Stir in the garlic.
Add the lentils and stir all together to coat in the olive oil.
Stir in the tomatoes. Add the carrots, bay leaves and enough water to come about an inch above the surface of the lentils. Bring to a simmer, reduce heat to low, cover the pot, and cook slowly for about an hour, until the lentils are very tender and the soup thick and dense. Add water or stock as needed as the lentils cook to make sure there is enough liquid in the pot. The soup should be thick.
Remove the bay leaves, season to taste with salt, and stir in the vinegar and petimezi, adjusting the seasoning to taste.
Serve drizzled with more olive oil if desired.
